Tensor network trial states for chiral topological phases in two dimensions and a no-go theorem in any dimension

Trial wavefunctions that can be represented by summing over locally-coupled degrees of freedom are called tensor network states (TNSs); they have seemed difficult to construct for two-dimensional topological phases that possess protected gapless edge excitations. We show it can be done for chiral states of free fermions, using a Gaussian Grassmann integral, yielding $p_x \pm i p_y$ and Chern insulator states, in the sense that the fermionic excitations live in a topologically non-trivial bundle of the required type. We prove that any strictly short-range quadratic parent Hamiltonian for these states is gapless; the proof holds for a class of systems in any dimension of space. The proof also shows, quite generally, that sets of compactly-supported Wannier-type functions do not exist for band structures in this class. We construct further examples of TNSs that are analogs of fractional (including non-Abelian) quantum Hall phases; it is not known whether parent Hamiltonians for these are also gapless.Comment: 5 pages plus 4 pages supplementary material, inc 3 figures. v2: improved no-go theorem, additional references. v3: changed to regular article format; 16 pages, 3 figures, no supplemental material; main change is much extended proof of no-go theorem. v4: minor changes; as-published versio

How to break the density-anisotropy degeneracy in spherical stellar systems

We present a new non-parametric Jeans code, GravSphere, that recovers the density $\rho(r)$ and velocity anisotropy $\beta(r)$ of spherical stellar systems, assuming only that they are in a steady-state. Using a large suite of mock data, we confirm that with only line-of-sight velocity data, GravSphere provides a good estimate of the density at the projected stellar half mass radius, $\rho(R_{1/2})$, but is not able to measure $\rho(r)$ or $\beta(r)$, even with 10,000 tracer stars. We then test three popular methods for breaking this $\rho-\beta$ degeneracy: using multiple populations with different $R_{1/2}$; using higher order `Virial Shape Parameters' (VSPs); and including proper motion data. We find that two populations provide an excellent recovery of $\rho(r)$ in-between their respective $R_{1/2}$. However, even with a total of $\sim 7,000$ tracers, we are not able to well-constrain $\beta(r)$ for either population. By contrast, using 1000 tracers with higher order VSPs we are able to measure $\rho(r)$ over the range $0.5 < r/R_{1/2} < 2$ and broadly constrain $\beta(r)$. Including proper motion data for all stars gives an even better performance, with $\rho$ and $\beta$ well-measured over the range $0.25 < r/R_{1/2} < 4$. Finally, we test GravSphere on a triaxial mock galaxy that has axis ratios typical of a merger remnant, $[1:0.8:0.6]$. In this case, GravSphere can become slightly biased. However, we find that when this occurs the data are poorly fit, allowing us to detect when such departures from spherical symmetry become problematic.Comment: 19 pages; 1 table; 11 Figures. Version accepted for publication in MNRAS. (Minor changes from previously. Appendix B added showing decreasing bias of VSP estimators with increasing sampling.

The X-ray Evolution of Merging Galaxies

We present here the first study of the X-ray properties of an evolutionary sample of merging galaxies. Both ROSAT PSPC and HRI data are presented for a sample of eight interacting galaxy systems, each believed to involve a similar encounter between two spiral discs of approximately equal size. The mergers span a large range in age, from completely detached to fully merged systems. A great deal of interesting X-ray structure is seen, and the X-ray properties of each individual system are discussed in detail. Along the merging sequence, several trends are evident: in the case of several of the infrared bright systems, the diffuse emission is very extended, and appears to arise from material ejected from the galaxies. The onset of this process seems to occur very soon after the galaxies first encounter one another, and these ejections soon evolve into distorted flows. More massive extensions (perhaps involving up to 1e10 solar masses of hot gas) are seen at the `ultraluminous' peak of the interaction, as the galactic nuclei coalesce. The amplitude of the evolution of the X-ray emission through a merger is markedly different from that of the infrared and radio emission however, and this, we believe, may well be linked with the large extensions of hot gas observed. The late, relaxed remnants, appear relatively devoid of gas, and possess an X-ray halo very different from that of typical ellipticals, a problem for the `merger hypothesis', whereby the merger of two disc galaxies results in an elliptical galaxy. However, these systems are still relatively young in terms of total merger lifetime, and they may still have a few Gyr of evolution to go through, before they resemble typical elliptical galaxies.Comment: 30 pages, 15 figures, accepted by MNRA

Exponents and bounds for uniform spanning trees in d dimensions

Uniform spanning trees are a statistical model obtained by taking the set of all spanning trees on a given graph (such as a portion of a cubic lattice in d dimensions), with equal probability for each distinct tree. Some properties of such trees can be obtained in terms of the Laplacian matrix on the graph, by using Grassmann integrals. We use this to obtain exact exponents that bound those for the power-law decay of the probability that k distinct branches of the tree pass close to each of two distinct points, as the size of the lattice tends to infinity.Comment: 5 pages. v2: references added. v3: closed form results can be extended slightly (thanks to C. Tanguy). v4: revisions, and a figure adde

Understanding the fidelity effect when evaluating games with children

There have been a number of studies that have compared evaluation results from prototypes of different fidelities but very few of these are with children. This paper reports a comparative study of three prototypes ranging from low fidelity to high fidelity within the context of mobile games, using a between subject design with 37 participants aged 7 to 9. The children played a matching game on either an iPad, a paper prototype using screen shots of the actual game or a sketched version. Observational data was captured to establish the usability problems, and two tools from the Fun Toolkit were used to measure user experience. The results showed that there was little difference for user experience between the three prototypes and very few usability problems were unique to a specific prototype. The contribution of this paper is that children using low-fidelity prototypes can effectively evaluate games of this genre and style

Animating the Real: Illusions, Musicality and the Live Dancing Body

Animation film frequently uses dance and choreography as part of explicit scenes to help assist with and compliment the narrative. Although animators frequently acknowledge relationships between dance and animation, scarcely any scholarly work considers how animated film principles are used and applied within live dance performances. Additionally, although many scholars discuss the relationship between live dance and music and similarly animation and music, rarely has the collision of all three been scrutinized. In this article, I draw upon principles from animation film and choreomusical scholarship to show a complex relationship between the real and the pretend in a solo street dance performance. Based on detailed movement analysis of a short solo dance performance by Isaac "Turbo" Baptiste, I discuss the ways that moving image can influence live dancing bodies and create endless possibilities for choreomusical play